Theoretical thermochemistry of some LiXHn and BeXHn compounds

Summary In this theoretical work, we consider the geometrical, electronic and energetic properties of some lithium and beryllium derivatives. The standard heats of formation of these compounds have been calculated at the MP4=SDTQ/6-31+G(2df, p)//MP2=FULL/6-31G(d, p) level. The values obtained at this level of the theory are also compared with the heats of formation deduced from a composite procedure in which it is assumed that some corrections can be treated separately and combined in an additive manner. We find that the values determined with the complete 6-31+G(2df, p) basis set are the more accurate.     

Etude theorique des effets de substituants dans les cycloadditions dipolaires-1,3

A theoretical study of substituent effects on 1,3-dipolar cycloadditions has been carried out by the LCAO-SCF-MO method. The potential energy hypersurfaces for ten reactions and the electronic and energetic properties of the transition states have been investigated.     

Some multivariate inequalities with applications

Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\cal {X}}_{n} =(X_1,\ldots,X_n)$ be a random vector. Suppose that the random variables $(X_i)_{1\leq i\leq n}$ are stationary and fulfill a suitable dependence criterion. Let $f$ be a real valued function defined on $\mathbbm{R}^n$ having some regular properties. Let ${\cal {Y}}_{n}$ be a random vector, independent of ${\cal {X}}_{n}$, having independent and identically distributed components. We control $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$. Suitable choices of the function $f$ yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995).     

Sur la densité d'état de l'opérateur de Schrödinger quasi-périodique unidimensionnel

We prove two results on the density of states of the discrete one dimensional quasi-periodic Schrödinger equation with an analytic potential and Diophantine frequencies in the perturbed regime. On the one hand, we prove that this function has the behavior of a Hölder-$\frac{1}{2}$ function. On the other, we show that the length of the gaps has a sub-exponential estimate which depends on its label given by the gap-labeling theorem. To cite this article: S. Hadj Amor, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

A note on nil power serieswise Armendariz rings

A ring R is called nil power serieswise Armendariz if $ \forall f = \sum\limits_{i = 0}^\infty {a_i X^i } $ \forall f = \sum\limits_{i = 0}^\infty {a_i X^i } and $ g = \sum\limits_{i = 0}^\infty {b_i X^i } $ g = \sum\limits_{i = 0}^\infty {b_i X^i } in R[[X]] such that f g ∈ Nil(R)[[X]], then a _i b _j ∈ Nil(R) for all i and j. In this note we characterize completely nil power serieswise Armendariz rings with their nilradical Nil(R) (where the nilradical is the set of nilpotent elements). We prove that a ring is nil power serieswise Armendariz if and only if Nil(R) is an ideal of R. We prove that each power serieswise Armendariz ring is nil power serieswise Armendariz and we give examples of nil power serieswise Armendariz rings.     

Post modification of zinc based coordination polymer to prepare Zn‐Mo‐ICP nanoparticles as efficient self‐supported catalyst for olefin epoxidation

Preparation, characterization, and catalytic properties of bimetallic coordination polymer constructed from 2‐aminoterephthalic acid as linker, zinc cations as node, and cis‐dioxo molybdenum units as catalytic active sites are reported via two pathways. Molybdenum centers were placed in N,O positions created by condensation reaction of 2‐aminoterephthalic acid with salicylaldehyde while zinc cations coordinated via carboxylic acid groups of linker to achieve infinite chains of metalo‐ligand. The obtained coordination polymer was fully characterized and its catalytic properties in the epoxidation of olefins with tert‐butyl hydroperoxide (TBHP) described. In comparison with previously reported heterogenized molybdenum catalysts, this new coordination polymer exhibited good conversion as well as high selectivity in the epoxidation of olefins. The catalyst is stable under ambient conditions and could be reused as active catalyst for at least five times.     

Magnetic Field-Assisted Direct Immersion SPME of Endogenous Aldehydes in Human Urine

Direct immersion solid-phase microextraction (DI-SPME) is an effective microsampling strategy for polar and ionic species in aqueous media. Nevertheless, the fiber coating is in direct contact with sample solution and affected by its conditions. To compensate this limitation and to improve the extraction efficiency, a magnetic fiber coating was prepared and employed for DI-SPME sampling under the enhancing effect of a magnetic field. Magnetic iron oxide core–shell silica nanoparticles were synthesized and embedded in polypyrrole using an in situ electropolymerization method along with simultaneous coating on the surface of a platinized stainless-steel fiber. It was then applied for magnetic-assisted DI-SPME (MA-DI-SPME) sampling of endogenous aldehydes in human urine. Sample solution pH, the magnetic field intensity, ionic strength and extraction time were evaluated as the important affecting variables. Limits of detection were obtained 0.01–0.1 ng mL^?1; the calibration graphs were linear over the range of 0.1–10000 ng mL^?1. The inter-fiber (fiber-to-fiber) reproducibility was found to be 10.7–12.5%. Matrix effect from urine samples was not observed at concentration levels of 0.2, 2, and 8 µg mL^?1. The results showed that magnetic field increased the efficiency of DI-SPME method about two to four times. The developed strategy was successfully applied for the extraction and quantification of hexanal and heptanal (as the most important aldehyde biomarkers) in urine samples.

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Evaluation of polypyrrole/silver/polyethylene glycol nanocomposite sorbent for electroenhanced direct-immersion solid-phase microextraction of carvacrol and thymol from medicinal plants

The unique features of nanostructured polypyrrole, conductivity enhancement effect of silver nanoparticles and high polar adsorptivity of polyethylene glycol were merged into polypyrrole/silver/polyethylene glycol (PPy/Ag/PEG) nanocomposite. It was synthesized and simultaneously coated on the surface of a stainless-steel fiber using an amended electropolymerization procedure. Before coating, the fiber substrate was made porous and sticky by allocating platinum dots on the surface of the stainless-steel fiber using the electrophoretic method. The prepared fiber was applied for the extraction of carvacrol and thymol (the most important antioxidants in medicinal plants) through an electroenhanced direct-immersion solid-phase microextraction (EE-DI-SPME) sampling strategy, followed by GC-FID quantification. To achieve the best efficiency, the effectual experimental variables including pH of sample solution, applied voltage, extraction temperature and time, stirring rate, and ionic strength were investigated. Under the optimal experimental conditions, the calibration curves were linear over the range of 0.5–30 µg mL^?1 for thymol and 0.01–30 µg mL^?1 for carvacrol. The detection limits (3S_b) and relative standard deviation (RSD%, n?=?6) were obtained to be 0.15, 0.003 µg mL^?1 and 10.2, 8.7% for thymol and carvacrol, respectively. The results demonstrated the priority of the proposed fiber compared with polypyrrole and polyacrylate fibers, in terms of extraction efficiency, durability and stability. The developed method was successfully employed for the analysis of thymol and carvacrol in medicinal plants.